**Mohammad Idris Qureshi and Shakir Hussain Malik**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 30, 2024, Number 3, Pages 499–515

DOI: 10.7546/nntdm.2024.30.3.499-515

**Full paper (PDF, 288 Kb)**

## Details

### Authors and affiliations

Mohammad Idris Qureshi

*Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University)
New Delhi, 110025, India*

Shakir Hussain Malik

*Department of Mathematics, Government Degree College
Magam Budgam, Jammu and Kashmir, 193401, India*

### Abstract

In this paper, we provide the analytical solutions of the families of certain definite integrals: and in terms of multiple hypergeometric functions of Kampé de Fériet having the arguments and Riemann zeta functions. As applications, we obtain some mixed summation formulas (19), (35) and (46) involving generalized hypergeometric functions and having the arguments and other (possibly) new summation formulas (38) and (40) for multiple hypergeometric functions of Kampé de Fériet having the arguments also mixed relations (36) and (47) involving Riemann zeta functions.

### Keywords

- Hypergeometric functions
- Log-cosine integrals
- Riemann zeta function
- Kampé de Fériet multiple hypergeometric functions

### 2020 Mathematics Subject Classification

- 33C05
- 33C20
- 11B65
- 11M06
- 33B20

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### Manuscript history

- Received: 30 May 2023
- Revised: 3 June 2024
- Accepted: 19 September 2024
- Online First: 26 September 2024

### Copyright information

Ⓒ 2024 by the Authors.

This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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## Cite this paper

Qureshi, M. I., & Malik, S. H. (2024). Evaluation of certain families of log-cosine integrals using hypergeometric function approach and applications. *Notes on Number Theory and Discrete Mathematics*, 30(3), 499-515, DOI: 10.7546/nntdm.2024.30.3.499-515.